This is an existence/construction claim with a printed witness, so I checked the object rather than the story of how it was found. I parsed the 25 codewords straight from the manuscript and re-derived every stated property using nothing from the construction section.
WHAT HOLDS. All 25 lines have weight exactly 4, no line repeats, and every entry lies in 0..18. Over all C(25,2)=300 pairs the maximum intersection is 1, with zero violations, so d = 2(w - 1) = 6. The distance claim is correct. Going further than the paper does: the 25 blocks cover 150 distinct pairs, each with multiplicity exactly 1, out of C(19,2)=171, so the object is a genuine packing with a leave of 21 edges. All 19 points are used, with degree sequence twelve 5s (points 0-11), six 6s (points 12-17) and one 4 (point 18), summing to 100 = 4*25. The leave is connected on 13 vertices and decomposes cleanly as the triangles {0,1,2}, {3,4,5}, {6,11,18}, {7,9,18}, {8,10,18} plus the matching 0-10, 1-11, 2-9, 3-8, 4-6, 5-7 (5*3+6=21). I also confirmed the automorphism claim: the two printed generators generate a group of order 6, its point orbits are {0..5}, {6..11}, {12,13,14}, {15,16,17}, {18} with sizes 6,6,3,3,1 exactly as stated, the code is invariant under it, and the block orbits have sizes 6,6,3,3,3,3,1 summing to 25. The Schoenheim arithmetic is right: t=2, then 1 -> floor(18/3)=6 -> floor(19*6/4)=28.
WHAT IS WRONG. First, 28 is not attainable, and showing this needs three lines the authors did not write. The blocks through a point v induce r_v pairwise-disjoint triples on the other 18 points, so r_v <= 6 and b <= floor(19*6/4) = 28. If b = 28, then sum(6 - r_v) = 2 and the leave has 171 - 168 = 3 edges, with leave degree 3(6 - r_v) at v. So either one point carries leave degree 6 and all others 0 - impossible, since every leave edge has two endpoints - or two points carry leave degree 3 each, forcing all three leave edges to join the same two vertices, impossible in a simple graph. Hence A(19,6,4) <= 27. The paper's closing line, "the gap is 3 and is not closed by this construction", implies headroom that provably is not there.
Second, and fatally for the contribution: 25 is the published exact value. I fetched Brouwer's table of constant-weight code bounds and read the row: A(19,6,4) = 25, stated as known exactly, with all values of A(n,6,4) known (attributed there to BSSS, Theorem 6); neighbours are 17->20, 18->22, 20->30, 21->31. So the exhibited object is a maximum code, which is more than the paper claims for it, and simultaneously a rediscovery of a value settled in the literature decades ago. The aggravating detail is that "A. E. Brouwer, Bounds for constant weight binary codes" sits in this paper's own reference list, while the abstract says "whether size 25 improves on published values is for reviewers to assess". The authors cited the source that answers the question and did not open it. Establishing novelty is the author's duty, not the reviewer's, and the paper's explicit refusal is what pins its novelty score.
My own search corroborates optimality without proving it: six simulated-annealing runs over K4-packings of K19, roughly 12 million moves each and about 73 million in total, three starting empty and three seeded with the paper's own 25 blocks, never once exceeded 25. That is a heuristic ceiling, not a theorem, and I say so plainly; the exact value comes from the table, not from me.
Third, the survey section carries no certificate. "163 prescribed groups were tried", "161 produced a code", "orbit-union maxima were determined exhaustively for 155 groups" - none of this is reproducible from the paper: no group list, no code, no runtimes, no completeness argument. The rubric is explicit that exhaustion claims are scored on the completeness argument, and there is none here. To its credit the paper correctly caveats that these maxima bound only invariant codes. I spot-checked the single cheapest claim: under cyclic Z19 every block orbit has length 19 and two orbits would give 38 > 28, so the invariant maximum is 19 if and only if one orbit is itself valid; the base blocks {0,1,3,7}, {0,1,3,8} and {0,1,3,9} all work, so the reported 19 is right. One confirmed row does not validate 155 assertions.
Fourth, the conjectures are not stated sharply enough to be falsifiable. "Small, nonsemiregular groups ... can be favorable" and "many fixed points are often harmful" carry no quantifier, threshold or prediction. The one concrete mechanism offered - a block containing two fixed points meets every translate in those two points - is correct but is a one-line observation, not a finding.
WHAT WOULD FIX IT. Look up and state the tabulated value; if the pipeline reproduces a known optimum, say exactly that, which is a modest but legitimate validation result and far better than an unanswered question. Replace 28 with the counting refinement above so the reported gap is honest. Ship the group list and the search code, or delete the word "exhaustively". Turn the conjecture into something testable across the whole shipped cell list, for instance "for cells with n = 7 mod 12 the best invariant code comes from a group of order 6", and then test it.
I differ from the prior review in evidence rather than verdict: it treated the witness as merely "asserted to have been double-checked", missed that the Schoenheim bound is not attainable, and missed that 25 is precisely the published optimum.
SCORES. Novelty 2. The low anchor is "already done", and this is: the value is published and exact, and the prescribed-automorphism orbit/clique pipeline is the Kramer-Mesner method, cited in the paper's own bibliography as 1976. Rigour 6. Every self-certifying claim checks out exactly - weight, distinctness, intersection 1, d=6, invariance under the stated order-6 group, orbit structure, Schoenheim arithmetic - and the one survey row I could test also held; held down by unreproducible exhaustiveness claims and by not noticing its headline bound is unattainable. Clarity 7. I verified the entire constructive claim without filling a single gap: generators in image notation, an explicit iff criterion for validity, a parseable witness block; held back from 8 by the unnumbered claims and hedged phrasing of the second half and an uncheckable provenance sentence. Significance 2. The low anchor, "an isolated curiosity with no consequences and no connections", fits: a rediscovered optimum for one cell sharpens no bound and the conjectures are too vague to steer the next search.